Your team is in Cape Town, SA and monitoring a well that’s being threatened by s
ID: 1732699 • Letter: Y
Question
Your team is in Cape Town, SA and monitoring a well that’s being threatened by saltwater. The well is pumping 45 L/s from an aquifer that has a hydraulic conductivity of 400 m/d, saturated thickness of 50-m, porosity of 0.2, and a specific yield of 0.15. If the well is screened to within 15-m of the bottom of the aquifer, what will be the thickness of the saltwater wedge under the well when the well is likely to become contaminated with saltwater? (State any assumptions for temperature and density)
Explanation / Answer
Step 1:
Q=45 L/sec
Q=3888 m3/day
K=400 m/day
Thickness=50 m
Porosity=0.2
Specific yield=0.15
Screening distance=15m from the bottom
Step 2:
Saquifer=Q/4X3.14XT[-0.5772-ln(r2S/4Tt)]
50=3888/4x3.14xT[-0.5772-ln(u)]
u is generally assumed as 0.1 ft/sec or 0.03m/sec
50=3888/4x3.14xT[-0.5772-ln(0.03)]
T=18.135m2/day
Step 3:
Actual drawdown of aquifer:
Saquifer=Q/4x3.14xT[-0.5772-lnu+0.999u-0.249u2+0.055u3-0.097u4+0.001u5]
Saquifer=3888/4x3.14x18.135[-0.5772-ln0.03+0.99(0.03)-0.249(0.03)2+0.055(0.03)3-0.097(0.03)4+0.001(0.03)5]
Saquifer=50.50m
Step 4:
Swell=Saquifer+0.5Saquifer
Swell=50.50+0.5(50.50)
Swell=75.75m
Step 5:
Thickness of salt water wedge=75.75-50.50=25.25m
At a distance of 25.25m the well water is likely to become contaminated with salt water
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